combinations problem

ok, so i'm having trouble with the following problem, so if anyone could help, i'd be grateful. i think that there's some kind of permutation needed for this (meaning n choose k), but i'm confused about how to use it.

A bowling team has 11 adults and 7 children. One night, they decide to divide themselves into 3 teams. The first will have 3 adults and 3 children. The second will have 4 adults and 2 children. The third will also have 4 adults and 2 children. In how many ways can the three teams be chosen?

I think you mean "combinations".
The order of the names on a team is not considered.

A bowling team has 11 adults and 7 children.
One night, they decide to divide themselves into 3 teams.. . The first will have 3 adults and 3 children.. . The second will have 4 adults and 2 children.. . The third will also have 4 adults and 2 children.

In how many ways can the three teams be chosen?

I will assume that the three teams are ordered and distinct.
That is, that they are called "Team #1", "Team #2", and "Team #3". **

Select team #1.
There are 11 adults; we choose 3 of them: ways.
There are 7 children; we choose 3 of them: ways.
Hence, there are: . ways to select team #1.

Select team #2.
There are 8 available adults; we choose 4 of them: ways.
There are 4 available children; we choose 2 of them: ways.
Hence, there are: . ways to select team #2.

The remaining 4 adults and 2 children will belong to team #3.

Therefore, there are: . ways to select the teams.

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** If teams #2 and #3 are interchangeable,. . . then the "420" is twice as large as it should be.